TSTP Solution File: GRP039-2 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 07:34:30 EDT 2022
% Result : Unsatisfiable 244.35s 244.77s
% Output : Refutation 244.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 14 09:00:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 123.24/123.68 *** allocated 10000 integers for termspace/termends
% 123.24/123.68 *** allocated 10000 integers for clauses
% 123.24/123.68 *** allocated 10000 integers for justifications
% 123.24/123.68 Bliksem 1.12
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Automatic Strategy Selection
% 123.24/123.68
% 123.24/123.68 Clauses:
% 123.24/123.68 [
% 123.24/123.68 [ =( multiply( identity, X ), X ) ],
% 123.24/123.68 [ =( multiply( inverse( X ), X ), identity ) ],
% 123.24/123.68 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 123.24/123.68 ],
% 123.24/123.68 [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) ) ],
% 123.24/123.68 [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~( =(
% 123.24/123.68 multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ],
% 123.24/123.68 [ =( multiply( X, identity ), X ) ],
% 123.24/123.68 [ =( multiply( X, inverse( X ) ), identity ) ],
% 123.24/123.68 [ 'subgroup_member'( X ), 'subgroup_member'( Y ), 'subgroup_member'(
% 123.24/123.68 'element_in_O2'( X, Y ) ) ],
% 123.24/123.68 [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X,
% 123.24/123.68 'element_in_O2'( X, Y ) ), Y ) ],
% 123.24/123.68 [ 'subgroup_member'( b ) ],
% 123.24/123.68 [ =( multiply( b, inverse( a ) ), c ) ],
% 123.24/123.68 [ =( multiply( a, c ), d ) ],
% 123.24/123.68 [ ~( 'subgroup_member'( d ) ) ]
% 123.24/123.68 ] .
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 percentage equality = 0.428571, percentage horn = 0.846154
% 123.24/123.68 This is a problem with some equality
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Options Used:
% 123.24/123.68
% 123.24/123.68 useres = 1
% 123.24/123.68 useparamod = 1
% 123.24/123.68 useeqrefl = 1
% 123.24/123.68 useeqfact = 1
% 123.24/123.68 usefactor = 1
% 123.24/123.68 usesimpsplitting = 0
% 123.24/123.68 usesimpdemod = 5
% 123.24/123.68 usesimpres = 3
% 123.24/123.68
% 123.24/123.68 resimpinuse = 1000
% 123.24/123.68 resimpclauses = 20000
% 123.24/123.68 substype = eqrewr
% 123.24/123.68 backwardsubs = 1
% 123.24/123.68 selectoldest = 5
% 123.24/123.68
% 123.24/123.68 litorderings [0] = split
% 123.24/123.68 litorderings [1] = extend the termordering, first sorting on arguments
% 123.24/123.68
% 123.24/123.68 termordering = kbo
% 123.24/123.68
% 123.24/123.68 litapriori = 0
% 123.24/123.68 termapriori = 1
% 123.24/123.68 litaposteriori = 0
% 123.24/123.68 termaposteriori = 0
% 123.24/123.68 demodaposteriori = 0
% 123.24/123.68 ordereqreflfact = 0
% 123.24/123.68
% 123.24/123.68 litselect = negord
% 123.24/123.68
% 123.24/123.68 maxweight = 15
% 123.24/123.68 maxdepth = 30000
% 123.24/123.68 maxlength = 115
% 123.24/123.68 maxnrvars = 195
% 123.24/123.68 excuselevel = 1
% 123.24/123.68 increasemaxweight = 1
% 123.24/123.68
% 123.24/123.68 maxselected = 10000000
% 123.24/123.68 maxnrclauses = 10000000
% 123.24/123.68
% 123.24/123.68 showgenerated = 0
% 123.24/123.68 showkept = 0
% 123.24/123.68 showselected = 0
% 123.24/123.68 showdeleted = 0
% 123.24/123.68 showresimp = 1
% 123.24/123.68 showstatus = 2000
% 123.24/123.68
% 123.24/123.68 prologoutput = 1
% 123.24/123.68 nrgoals = 5000000
% 123.24/123.68 totalproof = 1
% 123.24/123.68
% 123.24/123.68 Symbols occurring in the translation:
% 123.24/123.68
% 123.24/123.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 123.24/123.68 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 123.24/123.68 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 123.24/123.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 123.24/123.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 123.24/123.68 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 123.24/123.68 multiply [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 123.24/123.68 inverse [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 123.24/123.68 'subgroup_member' [45, 1] (w:1, o:23, a:1, s:1, b:0),
% 123.24/123.68 'element_in_O2' [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 123.24/123.68 b [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 123.24/123.68 a [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 123.24/123.68 c [49, 0] (w:1, o:15, a:1, s:1, b:0),
% 123.24/123.68 d [50, 0] (w:1, o:16, a:1, s:1, b:0).
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Starting Search:
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 3951
% 123.24/123.68 Kept: 2062
% 123.24/123.68 Inuse: 115
% 123.24/123.68 Deleted: 22
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 7376
% 123.24/123.68 Kept: 4081
% 123.24/123.68 Inuse: 164
% 123.24/123.68 Deleted: 26
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 11577
% 123.24/123.68 Kept: 6158
% 123.24/123.68 Inuse: 231
% 123.24/123.68 Deleted: 29
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 17354
% 123.24/123.68 Kept: 8188
% 123.24/123.68 Inuse: 287
% 123.24/123.68 Deleted: 33
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 22372
% 123.24/123.68 Kept: 10261
% 123.24/123.68 Inuse: 318
% 123.24/123.68 Deleted: 33
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 28960
% 123.24/123.68 Kept: 12344
% 123.24/123.68 Inuse: 346
% 123.24/123.68 Deleted: 39
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 35128
% 123.24/123.68 Kept: 14355
% 123.24/123.68 Inuse: 386
% 123.24/123.68 Deleted: 39
% 123.24/123.68 Deletedinuse: 14
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68 Resimplifying inuse:
% 123.24/123.68 Done
% 123.24/123.68
% 123.24/123.68
% 123.24/123.68 Intermediate Status:
% 123.24/123.68 Generated: 43921
% 123.24/123.68 Kept: 16444
% 244.35/244.77 Inuse: 456
% 244.35/244.77 Deleted: 97
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 47994
% 244.35/244.77 Kept: 18450
% 244.35/244.77 Inuse: 478
% 244.35/244.77 Deleted: 100
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying clauses:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 55647
% 244.35/244.77 Kept: 20549
% 244.35/244.77 Inuse: 492
% 244.35/244.77 Deleted: 2900
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 60017
% 244.35/244.77 Kept: 22662
% 244.35/244.77 Inuse: 508
% 244.35/244.77 Deleted: 2900
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 65325
% 244.35/244.77 Kept: 24846
% 244.35/244.77 Inuse: 537
% 244.35/244.77 Deleted: 2900
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 70223
% 244.35/244.77 Kept: 26866
% 244.35/244.77 Inuse: 562
% 244.35/244.77 Deleted: 2900
% 244.35/244.77 Deletedinuse: 66
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 74209
% 244.35/244.77 Kept: 28888
% 244.35/244.77 Inuse: 582
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 80584
% 244.35/244.77 Kept: 30932
% 244.35/244.77 Inuse: 610
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 85416
% 244.35/244.77 Kept: 33004
% 244.35/244.77 Inuse: 631
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 92835
% 244.35/244.77 Kept: 35030
% 244.35/244.77 Inuse: 673
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 101153
% 244.35/244.77 Kept: 37065
% 244.35/244.77 Inuse: 692
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 106903
% 244.35/244.77 Kept: 39362
% 244.35/244.77 Inuse: 712
% 244.35/244.77 Deleted: 2902
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying clauses:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 112296
% 244.35/244.77 Kept: 41418
% 244.35/244.77 Inuse: 734
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 125085
% 244.35/244.77 Kept: 43707
% 244.35/244.77 Inuse: 777
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 132818
% 244.35/244.77 Kept: 45724
% 244.35/244.77 Inuse: 811
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 140970
% 244.35/244.77 Kept: 47725
% 244.35/244.77 Inuse: 829
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 150519
% 244.35/244.77 Kept: 49759
% 244.35/244.77 Inuse: 856
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 157256
% 244.35/244.77 Kept: 51868
% 244.35/244.77 Inuse: 870
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 164012
% 244.35/244.77 Kept: 53882
% 244.35/244.77 Inuse: 882
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 172953
% 244.35/244.77 Kept: 55908
% 244.35/244.77 Inuse: 903
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 179595
% 244.35/244.77 Kept: 57968
% 244.35/244.77 Inuse: 918
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 185328
% 244.35/244.77 Kept: 60578
% 244.35/244.77 Inuse: 926
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying clauses:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 190003
% 244.35/244.77 Kept: 62850
% 244.35/244.77 Inuse: 936
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 194177
% 244.35/244.77 Kept: 65015
% 244.35/244.77 Inuse: 945
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 200238
% 244.35/244.77 Kept: 67252
% 244.35/244.77 Inuse: 957
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 206782
% 244.35/244.77 Kept: 69355
% 244.35/244.77 Inuse: 972
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 211565
% 244.35/244.77 Kept: 71357
% 244.35/244.77 Inuse: 984
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 217914
% 244.35/244.77 Kept: 73588
% 244.35/244.77 Inuse: 993
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 222690
% 244.35/244.77 Kept: 75759
% 244.35/244.77 Inuse: 999
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 228896
% 244.35/244.77 Kept: 77979
% 244.35/244.77 Inuse: 1005
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 237313
% 244.35/244.77 Kept: 80248
% 244.35/244.77 Inuse: 1037
% 244.35/244.77 Deleted: 2991
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying clauses:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 244635
% 244.35/244.77 Kept: 82874
% 244.35/244.77 Inuse: 1062
% 244.35/244.77 Deleted: 2992
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 268621
% 244.35/244.77 Kept: 85162
% 244.35/244.77 Inuse: 1158
% 244.35/244.77 Deleted: 2992
% 244.35/244.77 Deletedinuse: 68
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 281174
% 244.35/244.77 Kept: 87192
% 244.35/244.77 Inuse: 1199
% 244.35/244.77 Deleted: 3166
% 244.35/244.77 Deletedinuse: 240
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 287605
% 244.35/244.77 Kept: 89320
% 244.35/244.77 Inuse: 1233
% 244.35/244.77 Deleted: 3184
% 244.35/244.77 Deletedinuse: 256
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 292506
% 244.35/244.77 Kept: 92186
% 244.35/244.77 Inuse: 1247
% 244.35/244.77 Deleted: 3186
% 244.35/244.77 Deletedinuse: 257
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 297631
% 244.35/244.77 Kept: 94221
% 244.35/244.77 Inuse: 1273
% 244.35/244.77 Deleted: 3189
% 244.35/244.77 Deletedinuse: 257
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Intermediate Status:
% 244.35/244.77 Generated: 301445
% 244.35/244.77 Kept: 96274
% 244.35/244.77 Inuse: 1287
% 244.35/244.77 Deleted: 3193
% 244.35/244.77 Deletedinuse: 257
% 244.35/244.77
% 244.35/244.77 Resimplifying inuse:
% 244.35/244.77 Done
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 Bliksems!, er is een bewijs:
% 244.35/244.77 % SZS status Unsatisfiable
% 244.35/244.77 % SZS output start Refutation
% 244.35/244.77
% 244.35/244.77 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 244.35/244.77 , Z ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) )
% 244.35/244.77 ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.77 =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 5, [ =( multiply( X, identity ), X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 7, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X
% 244.35/244.77 , 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 9, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 10, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 11, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 12, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 14, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 15, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X,
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 20, [ 'subgroup_member'( inverse( b ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 25, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 46, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ), X
% 244.35/244.77 ), Y ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 49, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y )
% 244.35/244.77 ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 51, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) ),
% 244.35/244.77 'subgroup_member'( Y ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ), ~(
% 244.35/244.77 =( d, X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 58, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 65, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( b,
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 72, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 inverse( b ), X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 202, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 244.35/244.77 'subgroup_member'( T ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 209, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 211, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 d, X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 233, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 347, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X,
% 244.35/244.77 Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 350, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 244.35/244.77 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 352, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X )
% 244.35/244.77 , 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 460, [ ~( 'subgroup_member'( inverse( a ) ) ), 'subgroup_member'( c
% 244.35/244.77 ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 462, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X,
% 244.35/244.77 c ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 475, [ ~( 'subgroup_member'( a ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 835, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y )
% 244.35/244.77 ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 841, [ =( inverse( inverse( X ) ), X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 845, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 244.35/244.77 ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 853, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 860, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 244.35/244.77 multiply( X, X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 890, [ =( multiply( inverse( a ), d ), c ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 4219, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 4220, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.77 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 59529, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.77 multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 84862, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 244.35/244.77 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 84865, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 244.35/244.77 , =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 85308, [ 'subgroup_member'( Y ), ~( =( X, Y ) ), 'subgroup_member'(
% 244.35/244.77 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 85312, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.77 multiply( X, X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 85314, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 88837, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 89378, [ ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 89453, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.77 multiply( c, X ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 98079, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.77 .
% 244.35/244.77 clause( 98250, [] )
% 244.35/244.77 .
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 % SZS output end Refutation
% 244.35/244.77 found a proof!
% 244.35/244.77
% 244.35/244.77 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 244.35/244.77
% 244.35/244.77 initialclauses(
% 244.35/244.77 [ clause( 98252, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.77 , clause( 98253, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 , clause( 98254, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , clause( 98255, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , clause( 98256, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.77 , ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 98257, [ =( multiply( X, identity ), X ) ] )
% 244.35/244.77 , clause( 98258, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 244.35/244.77 , clause( 98259, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , clause( 98260, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =(
% 244.35/244.77 multiply( X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 , clause( 98261, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 , clause( 98262, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 , clause( 98263, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 , clause( 98264, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 ] ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.77 , clause( 98252, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 , clause( 98253, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98270, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 244.35/244.77 , Y ), Z ) ) ] )
% 244.35/244.77 , clause( 98254, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 244.35/244.77 , Z ) ) ] )
% 244.35/244.77 , clause( 98270, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply(
% 244.35/244.77 X, Y ), Z ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) )
% 244.35/244.77 ] )
% 244.35/244.77 , clause( 98255, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.77 =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 98256, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.77 , ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 5, [ =( multiply( X, identity ), X ) ] )
% 244.35/244.77 , clause( 98257, [ =( multiply( X, identity ), X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 244.35/244.77 , clause( 98258, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 7, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , clause( 98259, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.77 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X
% 244.35/244.77 , 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 , clause( 98260, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =(
% 244.35/244.77 multiply( X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.77 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 9, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 , clause( 98261, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 10, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 , clause( 98262, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 11, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 , clause( 98263, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 12, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 , clause( 98264, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98369, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqrefl(
% 244.35/244.77 clause( 98370, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 , clause( 98369, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, multiply( X, Y ) )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 14, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 , clause( 98370, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.77 , 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.77 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 factor(
% 244.35/244.77 clause( 98372, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 X, X ) ) ] )
% 244.35/244.77 , clause( 14, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.77 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 15, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X,
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , clause( 98372, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 X, X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98373, [ 'subgroup_member'( inverse( b ) ) ] )
% 244.35/244.77 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 244.35/244.77 ) ] )
% 244.35/244.77 , 0, clause( 9, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, b )] ), substitution( 1, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 20, [ 'subgroup_member'( inverse( b ) ) ] )
% 244.35/244.77 , clause( 98373, [ 'subgroup_member'( inverse( b ) ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98375, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 244.35/244.77 Y, Z ) ) ) ] )
% 244.35/244.77 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 244.35/244.77 ), Z ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98380, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 244.35/244.77 , identity ) ) ] )
% 244.35/244.77 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 , 0, clause( 98375, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 244.35/244.77 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98381, [ =( multiply( multiply( X, inverse( Y ) ), Y ), X ) ] )
% 244.35/244.77 , clause( 5, [ =( multiply( X, identity ), X ) ] )
% 244.35/244.77 , 0, clause( 98380, [ =( multiply( multiply( X, inverse( Y ) ), Y ),
% 244.35/244.77 multiply( X, identity ) ) ] )
% 244.35/244.77 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 244.35/244.77 :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.77 , clause( 98381, [ =( multiply( multiply( X, inverse( Y ) ), Y ), X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.77 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98384, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 244.35/244.77 Y, Z ) ) ) ] )
% 244.35/244.77 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 244.35/244.77 ), Z ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98386, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , clause( 11, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 , 0, clause( 98384, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, a ),
% 244.35/244.77 :=( Z, c )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 25, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 244.35/244.77 , clause( 98386, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98389, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98390, [ ~( =( X, multiply( inverse( b ), Y ) ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98389, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 1, clause( 20, [ 'subgroup_member'( inverse( b ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, inverse( b ) ), :=( Y, Y ), :=( Z, X )] ),
% 244.35/244.77 substitution( 1, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98393, [ ~( =( multiply( inverse( b ), Y ), X ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98390, [ ~( =( X, multiply( inverse( b ), Y ) ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 46, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ), X
% 244.35/244.77 ), Y ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 98393, [ ~( =( multiply( inverse( b ), Y ), X ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 244.35/244.77 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98394, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98396, [ ~( =( X, multiply( Y, inverse( Z ) ) ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , clause( 98394, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , 1, substitution( 0, [ :=( X, Y ), :=( Y, inverse( Z ) ), :=( Z, X )] ),
% 244.35/244.77 substitution( 1, [ :=( X, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98397, [ ~( =( multiply( Y, inverse( Z ) ), X ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , clause( 98396, [ ~( =( X, multiply( Y, inverse( Z ) ) ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 49, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y )
% 244.35/244.77 ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 244.35/244.77 , clause( 98397, [ ~( =( multiply( Y, inverse( Z ) ), X ) ), ~(
% 244.35/244.77 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98403, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98404, [ ~( =( X, multiply( b, Y ) ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.77 , 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98403, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 1, clause( 9, [ 'subgroup_member'( b ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, b ), :=( Y, Y ), :=( Z, X )] ),
% 244.35/244.77 substitution( 1, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98407, [ ~( =( multiply( b, Y ), X ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.77 , 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98404, [ ~( =( X, multiply( b, Y ) ) ), ~( 'subgroup_member'( Y )
% 244.35/244.77 ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 51, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) ),
% 244.35/244.77 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 98407, [ ~( =( multiply( b, Y ), X ) ), ~( 'subgroup_member'( Y )
% 244.35/244.77 ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 244.35/244.77 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98409, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98410, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 11, [ =( multiply( a, c ), d ) ] )
% 244.35/244.77 , 0, clause( 98409, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'(
% 244.35/244.77 X ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, c ),
% 244.35/244.77 :=( Z, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98411, [ ~( =( d, X ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98410, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ), ~(
% 244.35/244.77 =( d, X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 98411, [ ~( =( d, X ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 244.35/244.77 0 ), ==>( 2, 1 ), ==>( 3, 3 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98412, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ),
% 244.35/244.77 ~( =( d, X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqrefl(
% 244.35/244.77 clause( 98413, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ),
% 244.35/244.77 'subgroup_member'( d ) ] )
% 244.35/244.77 , clause( 98412, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 244.35/244.77 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, d )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98414, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , clause( 12, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 , 0, clause( 98413, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c
% 244.35/244.77 ) ), 'subgroup_member'( d ) ] )
% 244.35/244.77 , 2, substitution( 0, [] ), substitution( 1, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 58, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.77 , clause( 98414, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) )
% 244.35/244.77 ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98415, [ ~( =( Y, multiply( b, X ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 51, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) )
% 244.35/244.77 , 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqrefl(
% 244.35/244.77 clause( 98416, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 b, X ) ) ] )
% 244.35/244.77 , clause( 98415, [ ~( =( Y, multiply( b, X ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( b, X ) )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 65, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( b,
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , clause( 98416, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 b, X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98417, [ ~( =( Y, multiply( inverse( b ), X ) ) ), ~(
% 244.35/244.77 'subgroup_member'( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 46, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ),
% 244.35/244.77 X ), Y ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqrefl(
% 244.35/244.77 clause( 98418, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 inverse( b ), X ) ) ] )
% 244.35/244.77 , clause( 98417, [ ~( =( Y, multiply( inverse( b ), X ) ) ), ~(
% 244.35/244.77 'subgroup_member'( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( inverse( b ), X ) )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 72, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 inverse( b ), X ) ) ] )
% 244.35/244.77 , clause( 98418, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 inverse( b ), X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98419, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X ) )
% 244.35/244.77 , ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.77 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98420, [ ~( =( X, multiply( Y, Z ) ) ), ~( 'subgroup_member'( Z ) )
% 244.35/244.77 , 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( Y, T ) ) ] )
% 244.35/244.77 , clause( 98419, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 244.35/244.77 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , 1, clause( 7, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 244.35/244.77 substitution( 1, [ :=( X, Y ), :=( Y, T )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98431, [ ~( =( multiply( Y, Z ), X ) ), ~( 'subgroup_member'( Z ) )
% 244.35/244.77 , 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( Y, T ) ) ] )
% 244.35/244.77 , clause( 98420, [ ~( =( X, multiply( Y, Z ) ) ), ~( 'subgroup_member'( Z )
% 244.35/244.77 ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( Y, T ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 202, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 244.35/244.77 'subgroup_member'( T ) ] )
% 244.35/244.77 , clause( 98431, [ ~( =( multiply( Y, Z ), X ) ), ~( 'subgroup_member'( Z )
% 244.35/244.77 ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( Y, T ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 3 ), ==>( 1, 2 ), ==>( 2, 4 ), ==>( 3, 0 ),
% 244.35/244.77 ==>( 4, 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98465, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 244.35/244.77 , 'subgroup_member'( 'element_in_O2'( Y, X ) ) ] )
% 244.35/244.77 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 244.35/244.77 ) ] )
% 244.35/244.77 , 0, clause( 7, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 244.35/244.77 , X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 209, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.77 , clause( 98465, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y
% 244.35/244.77 ), 'subgroup_member'( 'element_in_O2'( Y, X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 2
% 244.35/244.77 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98470, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 d, X ) ) ] )
% 244.35/244.77 , clause( 12, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.77 , 0, clause( 7, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 244.35/244.77 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, d ), :=( Y, X )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 211, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 d, X ) ) ] )
% 244.35/244.77 , clause( 98470, [ 'subgroup_member'( X ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( d, X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 factor(
% 244.35/244.77 clause( 98473, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 244.35/244.77 , clause( 202, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 244.35/244.77 'subgroup_member'( T ) ] )
% 244.35/244.77 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 233, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.77 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 244.35/244.77 , clause( 98473, [ 'subgroup_member'( X ), 'subgroup_member'(
% 244.35/244.77 'element_in_O2'( Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y
% 244.35/244.77 , Z ), X ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98477, [ =( Y, multiply( X, 'element_in_O2'( X, Y ) ) ),
% 244.35/244.77 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply(
% 244.35/244.77 X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98479, [ 'subgroup_member'( inverse( X ) ), =( X, multiply( Y,
% 244.35/244.77 'element_in_O2'( Y, X ) ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 244.35/244.77 ) ] )
% 244.35/244.77 , 0, clause( 98477, [ =( Y, multiply( X, 'element_in_O2'( X, Y ) ) ),
% 244.35/244.77 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 244.35/244.77 , X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98480, [ =( multiply( Y, 'element_in_O2'( Y, X ) ), X ),
% 244.35/244.77 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 98479, [ 'subgroup_member'( inverse( X ) ), =( X, multiply( Y,
% 244.35/244.77 'element_in_O2'( Y, X ) ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 347, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X,
% 244.35/244.77 Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.77 , clause( 98480, [ =( multiply( Y, 'element_in_O2'( Y, X ) ), X ),
% 244.35/244.77 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 244.35/244.77 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98487, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 244.35/244.77 Y, Z ) ) ) ] )
% 244.35/244.77 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 244.35/244.77 ), Z ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98490, [ =( multiply( multiply( X, Y ), 'element_in_O2'( Y, Z ) ),
% 244.35/244.77 multiply( X, Z ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply(
% 244.35/244.77 X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 244.35/244.77 , 2, clause( 98487, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 244.35/244.77 :=( X, X ), :=( Y, Y ), :=( Z, 'element_in_O2'( Y, Z ) )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 350, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 244.35/244.77 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.77 , clause( 98490, [ =( multiply( multiply( X, Y ), 'element_in_O2'( Y, Z ) )
% 244.35/244.77 , multiply( X, Z ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 244.35/244.77 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 factor(
% 244.35/244.77 clause( 98501, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X
% 244.35/244.77 ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 244.35/244.77 , clause( 347, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X
% 244.35/244.77 , Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.77 , 0, 2, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 352, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X )
% 244.35/244.77 , 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 244.35/244.77 , clause( 98501, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse(
% 244.35/244.77 X ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.77 1 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98504, [ 'subgroup_member'( c ), ~( 'subgroup_member'( inverse( a )
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , clause( 10, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 , 0, clause( 65, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.77 b, X ) ) ] )
% 244.35/244.77 , 1, 1, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 460, [ ~( 'subgroup_member'( inverse( a ) ) ), 'subgroup_member'( c
% 244.35/244.77 ) ] )
% 244.35/244.77 , clause( 98504, [ 'subgroup_member'( c ), ~( 'subgroup_member'( inverse( a
% 244.35/244.77 ) ) ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98506, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 244.35/244.77 Y, Z ) ) ) ] )
% 244.35/244.77 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 244.35/244.77 ), Z ) ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98508, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X
% 244.35/244.77 , c ) ) ] )
% 244.35/244.77 , clause( 10, [ =( multiply( b, inverse( a ) ), c ) ] )
% 244.35/244.77 , 0, clause( 98506, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 244.35/244.77 multiply( Y, Z ) ) ) ] )
% 244.35/244.77 , 0, 9, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b ),
% 244.35/244.77 :=( Z, inverse( a ) )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 462, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X,
% 244.35/244.77 c ) ) ] )
% 244.35/244.77 , clause( 98508, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply(
% 244.35/244.77 X, c ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98511, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( inverse(
% 244.35/244.77 a ) ) ) ] )
% 244.35/244.77 , clause( 58, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , 1, clause( 460, [ ~( 'subgroup_member'( inverse( a ) ) ),
% 244.35/244.77 'subgroup_member'( c ) ] )
% 244.35/244.77 , 1, substitution( 0, [] ), substitution( 1, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98512, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( a ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , clause( 98511, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'(
% 244.35/244.77 inverse( a ) ) ) ] )
% 244.35/244.77 , 1, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 factor(
% 244.35/244.77 clause( 98513, [ ~( 'subgroup_member'( a ) ) ] )
% 244.35/244.77 , clause( 98512, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( a ) )
% 244.35/244.77 ] )
% 244.35/244.77 , 0, 1, substitution( 0, [] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 475, [ ~( 'subgroup_member'( a ) ) ] )
% 244.35/244.77 , clause( 98513, [ ~( 'subgroup_member'( a ) ) ] )
% 244.35/244.77 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98514, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ] )
% 244.35/244.77 , clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98517, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.77 , 0, clause( 98514, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , 0, 7, substitution( 0, [ :=( X, inverse( Y ) ), :=( Y, X )] ),
% 244.35/244.77 substitution( 1, [ :=( X, multiply( X, inverse( inverse( Y ) ) ) ), :=( Y
% 244.35/244.77 , Y )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 835, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y )
% 244.35/244.77 ) ] )
% 244.35/244.77 , clause( 98517, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X,
% 244.35/244.77 Y ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.77 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 eqswap(
% 244.35/244.77 clause( 98520, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ] )
% 244.35/244.77 , clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.77 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98522, [ =( inverse( inverse( X ) ), multiply( identity, X ) ) ] )
% 244.35/244.77 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.77 , 0, clause( 98520, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ]
% 244.35/244.77 )
% 244.35/244.77 , 0, 5, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 244.35/244.77 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98523, [ =( inverse( inverse( X ) ), X ) ] )
% 244.35/244.77 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.77 , 0, clause( 98522, [ =( inverse( inverse( X ) ), multiply( identity, X ) )
% 244.35/244.77 ] )
% 244.35/244.77 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.77 ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 841, [ =( inverse( inverse( X ) ), X ) ] )
% 244.35/244.77 , clause( 98523, [ =( inverse( inverse( X ) ), X ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 paramod(
% 244.35/244.77 clause( 98526, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse( X )
% 244.35/244.77 ) ) ] )
% 244.35/244.77 , clause( 841, [ =( inverse( inverse( X ) ), X ) ] )
% 244.35/244.77 , 0, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 244.35/244.77 X ) ) ] )
% 244.35/244.77 , 1, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 244.35/244.77 X ) )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 845, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 244.35/244.77 ) ] )
% 244.35/244.77 , clause( 98526, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse( X
% 244.35/244.77 ) ) ) ] )
% 244.35/244.77 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 244.35/244.77 0 )] ) ).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 resolution(
% 244.35/244.77 clause( 98527, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.77 , clause( 475, [ ~( 'subgroup_member'( a ) ) ] )
% 244.35/244.77 , 0, clause( 845, [ ~( 'subgroup_member'( inverse( X ) ) ),
% 244.35/244.77 'subgroup_member'( X ) ] )
% 244.35/244.77 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 244.35/244.77
% 244.35/244.77
% 244.35/244.77 subsumption(
% 244.35/244.77 clause( 853, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.78 , clause( 98527, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98528, [ 'subgroup_member'( multiply( X, X ) ), ~(
% 244.35/244.78 'subgroup_member'( inverse( X ) ) ) ] )
% 244.35/244.78 , clause( 15, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X
% 244.35/244.78 , X ) ) ] )
% 244.35/244.78 , 0, clause( 845, [ ~( 'subgroup_member'( inverse( X ) ) ),
% 244.35/244.78 'subgroup_member'( X ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 860, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98528, [ 'subgroup_member'( multiply( X, X ) ), ~(
% 244.35/244.78 'subgroup_member'( inverse( X ) ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 244.35/244.78 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98530, [ =( multiply( X, d ), multiply( multiply( X, a ), c ) ) ]
% 244.35/244.78 )
% 244.35/244.78 , clause( 25, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98533, [ =( multiply( inverse( a ), d ), multiply( identity, c ) )
% 244.35/244.78 ] )
% 244.35/244.78 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.78 , 0, clause( 98530, [ =( multiply( X, d ), multiply( multiply( X, a ), c )
% 244.35/244.78 ) ] )
% 244.35/244.78 , 0, 6, substitution( 0, [ :=( X, a )] ), substitution( 1, [ :=( X, inverse(
% 244.35/244.78 a ) )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98534, [ =( multiply( inverse( a ), d ), c ) ] )
% 244.35/244.78 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.78 , 0, clause( 98533, [ =( multiply( inverse( a ), d ), multiply( identity, c
% 244.35/244.78 ) ) ] )
% 244.35/244.78 , 0, 5, substitution( 0, [ :=( X, c )] ), substitution( 1, [] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 890, [ =( multiply( inverse( a ), d ), c ) ] )
% 244.35/244.78 , clause( 98534, [ =( multiply( inverse( a ), d ), c ) ] )
% 244.35/244.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98537, [ ~( =( Z, multiply( X, inverse( Y ) ) ) ), ~(
% 244.35/244.78 'subgroup_member'( X ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y
% 244.35/244.78 ) ) ] )
% 244.35/244.78 , clause( 49, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y
% 244.35/244.78 ) ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98539, [ ~( =( X, Y ) ), ~( 'subgroup_member'( multiply( Y, inverse(
% 244.35/244.78 inverse( Z ) ) ) ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z ) )
% 244.35/244.78 ] )
% 244.35/244.78 , clause( 24, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 244.35/244.78 , 0, clause( 98537, [ ~( =( Z, multiply( X, inverse( Y ) ) ) ), ~(
% 244.35/244.78 'subgroup_member'( X ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y
% 244.35/244.78 ) ) ] )
% 244.35/244.78 , 0, 3, substitution( 0, [ :=( X, inverse( Z ) ), :=( Y, Y )] ),
% 244.35/244.78 substitution( 1, [ :=( X, multiply( Y, inverse( inverse( Z ) ) ) ), :=( Y
% 244.35/244.78 , Z ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98540, [ ~( 'subgroup_member'( multiply( X, Y ) ) ), ~( =( Z, X ) )
% 244.35/244.78 , 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 244.35/244.78 , clause( 835, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y
% 244.35/244.78 ) ) ] )
% 244.35/244.78 , 0, clause( 98539, [ ~( =( X, Y ) ), ~( 'subgroup_member'( multiply( Y,
% 244.35/244.78 inverse( inverse( Z ) ) ) ) ), 'subgroup_member'( X ), ~(
% 244.35/244.78 'subgroup_member'( Z ) ) ] )
% 244.35/244.78 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 244.35/244.78 :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98541, [ ~( =( Y, X ) ), ~( 'subgroup_member'( multiply( Y, Z ) ) )
% 244.35/244.78 , 'subgroup_member'( X ), ~( 'subgroup_member'( Z ) ) ] )
% 244.35/244.78 , clause( 98540, [ ~( 'subgroup_member'( multiply( X, Y ) ) ), ~( =( Z, X )
% 244.35/244.78 ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 4219, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 244.35/244.78 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , clause( 98541, [ ~( =( Y, X ) ), ~( 'subgroup_member'( multiply( Y, Z ) )
% 244.35/244.78 ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 244.35/244.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 3 ), ==>( 2, 1 ), ==>( 3, 2 )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98542, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), ~(
% 244.35/244.78 'subgroup_member'( Z ) ), ~( 'subgroup_member'( multiply( X, Z ) ) ) ] )
% 244.35/244.78 , clause( 4219, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 244.35/244.78 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqrefl(
% 244.35/244.78 clause( 98543, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.78 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , clause( 98542, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), ~(
% 244.35/244.78 'subgroup_member'( Z ) ), ~( 'subgroup_member'( multiply( X, Z ) ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 4220, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.78 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , clause( 98543, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 244.35/244.78 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 244.35/244.78 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98544, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , clause( 853, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.78 , 0, clause( 4220, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.78 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ), :=( Y
% 244.35/244.78 , X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 59529, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , clause( 98544, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.78 1 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98546, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 244.35/244.78 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 244.35/244.78 ) ] )
% 244.35/244.78 , clause( 350, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 244.35/244.78 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98548, [ =( multiply( inverse( a ), X ), multiply( c,
% 244.35/244.78 'element_in_O2'( d, X ) ) ), 'subgroup_member'( d ), 'subgroup_member'( X
% 244.35/244.78 ) ] )
% 244.35/244.78 , clause( 890, [ =( multiply( inverse( a ), d ), c ) ] )
% 244.35/244.78 , 0, clause( 98546, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 244.35/244.78 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 244.35/244.78 ) ] )
% 244.35/244.78 , 0, 6, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ),
% 244.35/244.78 :=( Y, d ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98553, [ =( multiply( inverse( a ), X ), multiply( c,
% 244.35/244.78 'element_in_O2'( d, X ) ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 12, [ ~( 'subgroup_member'( d ) ) ] )
% 244.35/244.78 , 0, clause( 98548, [ =( multiply( inverse( a ), X ), multiply( c,
% 244.35/244.78 'element_in_O2'( d, X ) ) ), 'subgroup_member'( d ), 'subgroup_member'( X
% 244.35/244.78 ) ] )
% 244.35/244.78 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98554, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 244.35/244.78 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 98553, [ =( multiply( inverse( a ), X ), multiply( c,
% 244.35/244.78 'element_in_O2'( d, X ) ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 84862, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 244.35/244.78 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 98554, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 244.35/244.78 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.78 1 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98556, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 244.35/244.78 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 244.35/244.78 ) ] )
% 244.35/244.78 , clause( 350, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 244.35/244.78 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98559, [ =( multiply( X, Y ), multiply( identity, 'element_in_O2'(
% 244.35/244.78 inverse( X ), Y ) ) ), 'subgroup_member'( inverse( X ) ),
% 244.35/244.78 'subgroup_member'( Y ) ] )
% 244.35/244.78 , clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 244.35/244.78 , 0, clause( 98556, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 244.35/244.78 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 244.35/244.78 ) ] )
% 244.35/244.78 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 244.35/244.78 :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98564, [ =( multiply( X, Y ), 'element_in_O2'( inverse( X ), Y ) )
% 244.35/244.78 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.78 , 0, clause( 98559, [ =( multiply( X, Y ), multiply( identity,
% 244.35/244.78 'element_in_O2'( inverse( X ), Y ) ) ), 'subgroup_member'( inverse( X ) )
% 244.35/244.78 , 'subgroup_member'( Y ) ] )
% 244.35/244.78 , 0, 4, substitution( 0, [ :=( X, 'element_in_O2'( inverse( X ), Y ) )] ),
% 244.35/244.78 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98565, [ =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) )
% 244.35/244.78 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , clause( 98564, [ =( multiply( X, Y ), 'element_in_O2'( inverse( X ), Y )
% 244.35/244.78 ), 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 84865, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 244.35/244.78 , =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 244.35/244.78 , clause( 98565, [ =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y )
% 244.35/244.78 ), 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 244.35/244.78 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98569, [ ~( =( Z, multiply( X, Y ) ) ), 'subgroup_member'( Z ),
% 244.35/244.78 'subgroup_member'( 'element_in_O2'( X, Z ) ), ~( 'subgroup_member'( Y ) )
% 244.35/244.78 ] )
% 244.35/244.78 , clause( 233, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 244.35/244.78 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 244.35/244.78 , 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98571, [ ~( =( X, Y ) ), 'subgroup_member'( inverse( Y ) ),
% 244.35/244.78 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'( inverse( Y )
% 244.35/244.78 , X ) ), ~( 'subgroup_member'( 'element_in_O2'( inverse( Y ), Y ) ) ) ]
% 244.35/244.78 )
% 244.35/244.78 , clause( 352, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X
% 244.35/244.78 ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 244.35/244.78 , 1, clause( 98569, [ ~( =( Z, multiply( X, Y ) ) ), 'subgroup_member'( Z )
% 244.35/244.78 , 'subgroup_member'( 'element_in_O2'( X, Z ) ), ~( 'subgroup_member'( Y )
% 244.35/244.78 ) ] )
% 244.35/244.78 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, inverse(
% 244.35/244.78 Y ) ), :=( Y, 'element_in_O2'( inverse( Y ), Y ) ), :=( Z, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98665, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( 'subgroup_member'(
% 244.35/244.78 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , clause( 84865, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y
% 244.35/244.78 ), =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 244.35/244.78 , 2, clause( 98571, [ ~( =( X, Y ) ), 'subgroup_member'( inverse( Y ) ),
% 244.35/244.78 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'( inverse( Y )
% 244.35/244.78 , X ) ), ~( 'subgroup_member'( 'element_in_O2'( inverse( Y ), Y ) ) ) ]
% 244.35/244.78 )
% 244.35/244.78 , 3, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 244.35/244.78 :=( X, Y ), :=( Y, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98669, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 Y ), ~( 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , clause( 98665, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( 'subgroup_member'(
% 244.35/244.78 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , 1, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98671, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), ~(
% 244.35/244.78 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , clause( 98669, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 Y ), ~( 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , 2, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98945, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( inverse( X ) ) ] )
% 244.35/244.78 , clause( 98671, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), ~(
% 244.35/244.78 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 244.35/244.78 , 4, clause( 209, [ 'subgroup_member'( X ), 'subgroup_member'(
% 244.35/244.78 'element_in_O2'( X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 244.35/244.78 , inverse( X ) ), :=( Y, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98946, [ ~( =( Y, X ) ), 'subgroup_member'( multiply( Y, X ) ),
% 244.35/244.78 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( X ),
% 244.35/244.78 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.78 , clause( 98945, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( inverse( X ) ) ] )
% 244.35/244.78 , 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98954, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ) ] )
% 244.35/244.78 , clause( 98946, [ ~( =( Y, X ) ), 'subgroup_member'( multiply( Y, X ) ),
% 244.35/244.78 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( X ),
% 244.35/244.78 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 244.35/244.78 , 2, 4, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98956, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , clause( 98954, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ) ] )
% 244.35/244.78 , 2, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 85308, [ 'subgroup_member'( Y ), ~( =( X, Y ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.78 , clause( 98956, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 244.35/244.78 ), ==>( 1, 3 ), ==>( 2, 2 ), ==>( 3, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98963, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 244.35/244.78 , clause( 85308, [ 'subgroup_member'( Y ), ~( =( X, Y ) ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( multiply( X, Y ) )
% 244.35/244.78 ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqrefl(
% 244.35/244.78 clause( 98964, [ 'subgroup_member'( X ), 'subgroup_member'( inverse( X ) )
% 244.35/244.78 , 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98963, [ ~( =( Y, X ) ), 'subgroup_member'( Y ),
% 244.35/244.78 'subgroup_member'( inverse( X ) ), 'subgroup_member'( multiply( X, Y ) )
% 244.35/244.78 ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98965, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 244.35/244.78 ) ] )
% 244.35/244.78 , 0, clause( 98964, [ 'subgroup_member'( X ), 'subgroup_member'( inverse( X
% 244.35/244.78 ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98968, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98965, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 inverse( X ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 85312, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98968, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.78 1 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98969, [ 'subgroup_member'( multiply( X, X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 860, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , 0, clause( 85312, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98970, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98969, [ 'subgroup_member'( multiply( X, X ) ), 'subgroup_member'(
% 244.35/244.78 multiply( X, X ) ) ] )
% 244.35/244.78 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 85314, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , clause( 98970, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 eqswap(
% 244.35/244.78 clause( 98972, [ =( multiply( X, c ), multiply( multiply( X, b ), inverse(
% 244.35/244.78 a ) ) ) ] )
% 244.35/244.78 , clause( 462, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X
% 244.35/244.78 , c ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98975, [ =( multiply( inverse( b ), c ), multiply( identity,
% 244.35/244.78 inverse( a ) ) ) ] )
% 244.35/244.78 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 244.35/244.78 , 0, clause( 98972, [ =( multiply( X, c ), multiply( multiply( X, b ),
% 244.35/244.78 inverse( a ) ) ) ] )
% 244.35/244.78 , 0, 6, substitution( 0, [ :=( X, b )] ), substitution( 1, [ :=( X, inverse(
% 244.35/244.78 b ) )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98976, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 244.35/244.78 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 244.35/244.78 , 0, clause( 98975, [ =( multiply( inverse( b ), c ), multiply( identity,
% 244.35/244.78 inverse( a ) ) ) ] )
% 244.35/244.78 , 0, 5, substitution( 0, [ :=( X, inverse( a ) )] ), substitution( 1, [] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 88837, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 244.35/244.78 , clause( 98976, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 244.35/244.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98979, [ 'subgroup_member'( inverse( a ) ), ~( 'subgroup_member'( c
% 244.35/244.78 ) ) ] )
% 244.35/244.78 , clause( 88837, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 244.35/244.78 , 0, clause( 72, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 244.35/244.78 inverse( b ), X ) ) ] )
% 244.35/244.78 , 1, 1, substitution( 0, [] ), substitution( 1, [ :=( X, c )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98980, [ ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.78 , clause( 853, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 244.35/244.78 , 0, clause( 98979, [ 'subgroup_member'( inverse( a ) ), ~(
% 244.35/244.78 'subgroup_member'( c ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 89378, [ ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.78 , clause( 98980, [ ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98981, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( c, X ) ) ) ] )
% 244.35/244.78 , clause( 89378, [ ~( 'subgroup_member'( c ) ) ] )
% 244.35/244.78 , 0, clause( 4220, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ),
% 244.35/244.78 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, c ), :=( Y, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 89453, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( c, X ) ) ) ] )
% 244.35/244.78 , clause( 98981, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( c, X ) ) ) ] )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 244.35/244.78 1 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98984, [ ~( 'subgroup_member'( multiply( c, 'element_in_O2'( d, X )
% 244.35/244.78 ) ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 89453, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( c, X ) ) ) ] )
% 244.35/244.78 , 0, clause( 211, [ 'subgroup_member'( X ), 'subgroup_member'(
% 244.35/244.78 'element_in_O2'( d, X ) ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, 'element_in_O2'( d, X ) )] ), substitution(
% 244.35/244.78 1, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 paramod(
% 244.35/244.78 clause( 98986, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 244.35/244.78 'subgroup_member'( X ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 84862, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 244.35/244.78 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , 0, clause( 98984, [ ~( 'subgroup_member'( multiply( c, 'element_in_O2'( d
% 244.35/244.78 , X ) ) ) ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98987, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 244.35/244.78 'subgroup_member'( X ) ] )
% 244.35/244.78 , clause( 98986, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 244.35/244.78 'subgroup_member'( X ), 'subgroup_member'( X ) ] )
% 244.35/244.78 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98988, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ), ~(
% 244.35/244.78 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , clause( 59529, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 244.35/244.78 multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , 0, clause( 98987, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) )
% 244.35/244.78 , 'subgroup_member'( X ) ] )
% 244.35/244.78 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 244.35/244.78 ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 factor(
% 244.35/244.78 clause( 98989, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , clause( 98988, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 244.35/244.78 ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 98079, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 244.35/244.78 , clause( 98989, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 244.35/244.78 )
% 244.35/244.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 resolution(
% 244.35/244.78 clause( 98990, [] )
% 244.35/244.78 , clause( 98079, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 244.35/244.78 )
% 244.35/244.78 , 0, clause( 85314, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 244.35/244.78 , 0, substitution( 0, [ :=( X, inverse( a ) )] ), substitution( 1, [ :=( X
% 244.35/244.78 , inverse( a ) )] )).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 subsumption(
% 244.35/244.78 clause( 98250, [] )
% 244.35/244.78 , clause( 98990, [] )
% 244.35/244.78 , substitution( 0, [] ), permutation( 0, [] ) ).
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 end.
% 244.35/244.78
% 244.35/244.78 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 244.35/244.78
% 244.35/244.78 Memory use:
% 244.35/244.78
% 244.35/244.78 space for terms: 1344664
% 244.35/244.78 space for clauses: 4625557
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 clauses generated: 305028
% 244.35/244.78 clauses kept: 98251
% 244.35/244.78 clauses selected: 1311
% 244.35/244.78 clauses deleted: 3200
% 244.35/244.78 clauses inuse deleted: 257
% 244.35/244.78
% 244.35/244.78 subsentry: 6497776
% 244.35/244.78 literals s-matched: 2372840
% 244.35/244.78 literals matched: 1969599
% 244.35/244.78 full subsumption: 1104212
% 244.35/244.78
% 244.35/244.78 checksum: 152325437
% 244.35/244.78
% 244.35/244.78
% 244.35/244.78 Bliksem ended
%------------------------------------------------------------------------------